Regret-Optimal Policies for Rental Caches

We study the online caching problem in the setting where the service provider has access to a third-party rental cache that it can use via short-term contracts. The cost incurred to run this service is modelled as the sum of the rent cost incurred and the number of requests not served by the cache. We consider both stochastic and adversarial arrivals. Time is divided into slots, and in each time-slot, the algorithmic challenge is two-fold: (i) we first decide whether we want to rent the cache; and (ii) if we decide to rent, we determine which files to cache. We use regret to evaluate the performance of online caching policies with the optimal static caching policy as the benchmark. We propose a variant of the widely studied Follow the Perturbed Leader policy and show that it has order-optimal regret for both stochastic and adversarial arrivals. We supplement our analytical results with simulations using synthetic and trace-based request arrival sequences.